# Complex Evolution Recurrent Neural Networks (ceRNNs)

arXiv: https://arxiv.org/abs/1906.02246 · HTML: https://mlsanity.com/paper/1906.02246/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Jun 2019.

## Built on by (most cited first, 6 of 6)

- [A Survey of Complex-Valued Neural Networks](https://mlsanity.com/paper/2101.12249/) (2021)
- [A Survey of Deep Learning for Complex Speech Spectrograms](https://mlsanity.com/paper/2505.08694/) (2025)
- [Steinmetz Neural Networks for Complex-Valued Data](https://mlsanity.com/paper/2409.10075/) (2024)
- [Governance-Aware Hybrid Fine-Tuning for Multilingual Large Language Models](https://mlsanity.com/paper/2512.17344/) (2025)
- [Neural Controlled Differential Equations with Quantum Hidden Evolutions](https://mlsanity.com/paper/2404.19673/) (2024)
- [Hybrid and Unitary PEFT for Resource-Efficient Large Language Models](https://mlsanity.com/paper/2507.18076/) (2025)

## Abstract (arXiv)

Unitary Evolution Recurrent Neural Networks (uRNNs) have three attractive properties: (a) the unitary property, (b) the complex-valued nature, and (c) their efficient linear operators. The literature so far does not address -- how critical is the unitary property of the model? Furthermore, uRNNs have not been evaluated on large tasks. To study these shortcomings, we propose the complex evolution Recurrent Neural Networks (ceRNNs), which is similar to uRNNs but drops the unitary property selectively. On a simple multivariate linear regression task, we illustrate that dropping the constraints improves the learning trajectory. In copy memory task, ceRNNs and uRNNs perform identically, demonstrating that their superior performance over LSTMs is due to complex-valued nature and their linear operators. In a large scale real-world speech recognition, we find that pre-pending a uRNN degrades the performance of our baseline LSTM acoustic models, while pre-pending a ceRNN improves the performance over the baseline by 0.8% absolute WER.